1. Field of the Invention
This invention pertains generally to modeling of mathematical problems with analog electrical circuits, and more particularly to the modeling of Linear Programming (LP) problems, Quadratic Programming (QP) problems, and Model Predictive Control (MPC) problems with analog electrical circuits.
2. Description of Related Art
Analog circuits for solving optimization problems have been extensively studied in the past.
Renewed interest has stemmed from Model Predictive Control (MPC). In MPC, at each sampling time, starting at an initial current state, an open-loop optimal control problem is solved over a finite horizon. The optimal command signal is applied to the process only during the following sampling interval. At the next time step, a new optimal control problem based on new measurements of the state is solved over a shifted time horizon.
The optimal solution relies on a dynamic model of the process, respects input and output constraints, and minimizes a performance index. When the model is linear and the performance index is based on two-norm, one-norm, or ∞-norm, the resulting optimization problem can be cast as a linear programming (LP) problem or a quadratic programming (QP) problem, where the state enters the right hand side (rhs) of the constraints.